Question

87.5% decomposition of a radioactive substance complete in 3 hours. What is the half-life of that substance?

• A. 2 hours
• B. 3 hours
• C. 90 minutes
• D. 1 hours

Answer 1

Answer: (D)

Given, $N_0=100,N=100-87.5=12.5,$ $t=3hours,t_{1/2}=?$ We know that $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{\frac{t}{t_{1/2}}}$ $\frac{12.5}{100}={\left(\frac{1}{2}\right)}^{3/t_{1/2}}$ or ${\left(\frac{1}{2}\right)}^3={\left(\frac{1}{2}\right)}^{3/t_{1/2}}$ Hence, $\frac{3}{t_{1/2}}=3$ or $t_{1/2}=\frac{3}{3}=1hour$